The coupling of Yang-Mills to extended objects

doi:10.1016/0370-2693(92)90391-G

Physics Letters B

Volume 279, Issues 3–4, 16 April 1992, Pages 265-271

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Abstract

The coupling of Yang-Mills fields to the heterotic string in bosonic formulation is generalized to extended objects of higher dimension (p-branes). For odd p, the Bianchi identities obeyed by the field strengths of the (p+1)-forms receive Chern-Simons corrections which, in the case of the five-brane, are consistent with an earlier conjecture based on string/five-brane duality.

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Actions for extended objects based on Transgression and Chern-Simons forms for space-time groups and supergroups provide a gauge theoretic framework in which to embed previously studied String and Brane actions, extending them in interesting ways that may be useful in a future non perturbative formulation of String Theory. In this Letter I investigate aspects of the actions of these theories, including equations of motion and boundary conditions, gauge and space-time symmetries, and Dirac quantization of tensions. This theoretical framework is shown to include in certain limit and for a suitable gauge group the standard Bosonic String Theory.
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The purpose of this paper is to continue the study of the class of models proposed in a previous letter. The model corresponds to a system of branes of diverse dimensionalities with Chern–Simons actions for a supergroup, embedded in a background described also by a Chern–Simons action. The model treats the background and the branes on an equal footing, providing a “brane-target space democracy”. Here we suggest some possible extensions of the original model, and discuss its equations of motion, as well as the issue of currents and charges carried by the branes. We also discuss the relationship with M-theory and Superstring theory.
Fundamental extended objects for Chern-Simons supergravity
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We propose a class of models in which extended objects are introduced in Chern–Simons supergravity in such a way that those objects appear on the same footing as the target space. This is motivated by the idea that branes are already first quantized object, so that it is desirable to have a formalism that treats branes and their target space in a similar fashion. Accordingly, our models describe interacting branes, as gauge systems for supergroups. We also consider the case in which those objects have boundaries, and discuss possible links to superstring theory and/or M-theory, by studying the fermionic κ-symmetry of the action.
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We discuss a previously discovered [1] extension of the infinite-dimensional Lie algebra Map(M, g) which generalizes the Kac-Moody algebras in 1+1 dimensions and the Mickelsson-Faddeev algebras in 3+1 dimensions to manifolds M of general dimensions. Furthermore, we review the method of regularizing current algebras in higher dimensions using pseudodifferential operator (PSDO) symbol calculus. In particular, we discuss the issue of Lie algebra cohomology of PSDOs and its relation to the Schwinger terms arising in the quantization process. Finally, we apply this regularization method to the algebra of ref. [1] with partial success, and discuss the remaining obstacles to the construction of a Fock space representation.
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Membrane/ fivebrane duality in D = 11 implies Type IIA string/Type IIA fivebrane duality in D = 10, which in turn implies Type HA string/heterotic string duality in D = 6. To test the conjecture, we reproduce the corrections to the 3-form field equations of the D = 10 Type IIA string (a mixture of tree-level and one-loop effects) starting from the Chern-Simons corrections to the 7-form Bianchi identities of the D = 11 fivebrane (a purely tree-level effect). K3 compactification of the latter then yields the familiar gauge and Lorentz Chem-Simons corrections to 3-form Bianchi identities of the heterotic string. We note that the absence of a dilaton in the D = 11 theory allows us to fix both the gravitational constant and the fivebrane tension in terms of the membrane tension. We also comment on an apparent conflict between fundamental and solitonic heterotic strings and on the puzzle of a fivebrane origin of S-duality.
String solitons
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We review the status of solitons in superstring theory, with a view to understanding the strong coupling regime. These solitonic solutions are non-singular field configurations which solve the empty-space low-energy field equations (generalized, whenever possible, to all orders in α′), carry a non-vanishing topological “magnetic” charge and are stabilized by a topological conservation law. They are compared and contrasted with the elementary solutions which are singular solutions of the field equations with a σ-model source term and carry a non-vanishing Noether “electric” charge. In both cases, the solutions of most interest are those which preserve half the space-time supersymmetries and saturate a Bogomol'nyi bound. They typically arise as the extreme mass = charge limit of more general two-parameter solutions with event horizons. We also describe the theory dual to the fundamental string for which the roles of elementary and soliton solutions are interchanged. In 10 space-time dimensions, this dual theory is a superfivebrane and this gives rise to a string/fivebrane duality conjecture according to which the fivebrane may be regarded as fundamental in its own right, with the strongly coupled string corresponding to the weakly coupled fivebrane and vice versa. After compactification to four space-time dimensions, the fivebrane appears as a magnetic monopole or a dual string according as it wraps around five or four of the compactified dimensions. This gives rise to a four-dimensional string/string duality conjecture which subsumes a Montonen-Olive type duality in that the magnetic monopoles of the fundamental string correspond to the electric winding states of the dual string. This leads to a duality of dualities whereby under string/string duality the strong/weak coupling S-duality trades places with the minimum/maximum length T-duality. Since these magnetic monopoles are extreme black holes, a prediction of S-duality is that the corresponding electric massive states of the fundamental string are also extreme black holes. This is indeed the case.

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¹: Work supported in part by NSF grant PHY-9106593.

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The coupling of Yang-Mills to extended objects

Abstract

Nucl. Phys. B

Nucl. Phys. B

Phys. Lett. B

Phys. Lett. B

Phys. Lett. B